Probability distribution function

Definition

A Probability Distribution Function (PDF) for a discrete random variable is a function that provides the probabilities of occurrence of different possible outcomes. The sum of all probabilities in a PDF equals 1.

5 Must Know Facts For Your Next Test

1. The PDF for a discrete random variable lists each possible value the variable can take and its corresponding probability.
2. The total sum of all the probabilities in a PDF must be equal to 1: $$\sum P(x_i) = 1$$.
3. Each individual probability in the PDF must be between 0 and 1, inclusive: $$0 \leq P(x) \leq 1$$.
4. To find the probability of an event occurring within a range, sum the probabilities of all individual outcomes within that range.
5. The mean (expected value) of a discrete random variable can be calculated using its PDF: $$E(X) = \sum x_i P(x_i)$$.

Review Questions

• What is the requirement for the sum of all probabilities in a Probability Distribution Function?
• How do you calculate the expected value (mean) using a Probability Distribution Function?
• Why must each probability in a PDF for a discrete random variable lie between 0 and 1?

Related terms

Discrete Random Variable:

A type of random variable that can take on only specific, distinct values.

Cumulative Distribution Function (CDF):

A function representing the probability that a discrete random variable will take on a value less than or equal to a particular value.

Expected Value:

The mean or average value expected from repeated trials of an experiment; calculated as $$E(X) = \sum x_i P(x_i)$$ for discrete random variables.